Robust Discrete-Time Gain-Scheduled PSD Controller Design

Proportional, Integral, and Derivative (PID) and discrete-time Proportional, Summation, and Difference (PSD) controllers are most widely used in industry due to their simplicity and performance characteristics. However, with these conventional fixed gain controllers we could have difficulties to handle nonlinear or time-variant characteristics. This problem led to a various gain-scheduled PID/PSD controller design techniques in both state-space and frequency domain. For the gain-scheduled PID/PSD controller design in the state-space, the bilinear/linear matrix inequality-, and the Bellman-Lyapunov function-based approaches, obviously lead to a non-convex performance and stability conditions with respect to scheduled parameter. To overcome the problem of non-convex design procedure, several approaches were developed based on convexifications, which introduced some conservativeness in the gain-scheduled PID/PSD controller design. In this paper, a novel methodology is proposed for robust discrete-time output feedback gain-scheduled PSD controller design for uncertain linear parameter-varying systems with hard input constraints, and with a realistic scenario, when the output is noise corrupted. The proposed design procedure guarantees the robust affine parameter-dependent quadratic stability and the parameter-varying guaranteed cost (H2 performance) for a prescribed rate of change of scheduled parameters. Conditions to guarantee robust stability and performance requirements are translated directly to a convex optimization problem (without convexification) subject to linear matrix inequality constraints. A numerical example shows the benefit of the proposed method